First-Order Logic Chapter 8
First-Order Logic Chapter 8
Outline ·Vhy FOL? Syntax and semantics of FOL ·Using FOL ·Vumpus world in FOL Knowledge engineering in FOL
Outline • Why FOL? • Syntax and semantics of FOL • Using FOL • Wumpus world in FOL • Knowledge engineering in FOL
Pros and cons of propositional logic Propositional logic is declarative Propositional logic allows partial/disjunctive/negated information -(unlike most data structures and databases) Propositional logic is compositional: © -meaning of B1.1A P12 is derived from meaning of B1.1 and of P1.2 Meaning in propositional logic is context-independent -(unlike natural language,where meaning depends on context) Propositional logic has very limited expressive power
Pros and cons of propositional logic ☺ Propositional logic is declarative ☺ Propositional logic allows partial/disjunctive/negated information – (unlike most data structures and databases) – ☺ Propositional logic is compositional: ☺ – meaning of B1,1 P1,2 is derived from meaning of B1,1 and of P1,2 – ☺ Meaning in propositional logic is context-independent – (unlike natural language, where meaning depends on context) – Propositional logic has very limited expressive power
First-order logic Whereas propositional logic assumes the world contains facts, first-order logic (like natural language) assumes the world contains ● -Objects:people,houses,numbers,colors, baseball games,wars,.. -Relations:red,round,prime,brother of, bigger than,part of,comes between,.. -Functions:father of,best friend,one more than nlue
First-order logic • Whereas propositional logic assumes the world contains facts, • first-order logic (like natural language) assumes the world contains • – Objects: people, houses, numbers, colors, baseball games, wars, … – – Relations: red, round, prime, brother of, bigger than, part of, comes between, … – Functions: father of, best friend, one more than, plus, …
Syntax of FOL:Basic elements ·Constants KingJohn,2,NUS,... ·Predicates Brother,>,.. 。Functions Sqrt,LeftLegof,... 。Variables X,y;a,b,... ·Connectives,→，入，V,→ ·Equality ·Quantifiers V,J
Syntax of FOL: Basic elements • Constants KingJohn, 2, NUS,... • Predicates Brother, >,... • Functions Sqrt, LeftLegOf,... • Variables x, y, a, b,... • Connectives , , , , • Equality = • Quantifiers ,